The Lowe's Home Improvement site has a tutorial on how to clean clogged drain pipes without a snake. To do so, clean the drain pipe strainer, and use a plunger or chemical drain cleaners to unclog the drain pipe.
A clogged pipe often occurs due to a dirty pipe strainer. To clean a drain pipe strainer, remove the strainer by unscrewing it, and wash out any debris. Clean sink stoppers regularly to prevent clogged drains.
To unclog a drain pipe using a plunger, block any openings by stuffing wet rags into them. Make sure there is water in the basin, and apply petroleum jelly to the rim of the plunger. Use the plunger on the drain for a minute or two. Test the drain, and plunge again if it is still clogged. Run hot water to remove any debris from the drain when finished. A plunger only clears debris close to the main pipe, so a snake or chemical cleaners are needed for clogs further down the pipe.
To unclog a drain pipe using chemical drain cleaners, follow the instructions on the bottle, and make sure to run enough water afterwards to remove the chemicals. Drain cleaners have chemicals such as lye and sulfuric acid and can be dangerous if used incorrectly.
Keep drain pipes unclogged by running plenty of water when using a food disposer. Use drain cleaners every six months to keep the drains clear of debris.